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arXiv:nucl-th/9512042 · Physical Review C

Momentum distribution in nuclear matter within a perturbation approximation

A. Mariano, Francisco Krmpotić, A. F. R. de Toledo Piza

Published Apr 1, 1996• 6 citations
arXivHTMLPDF

Abstract

It is shown that the norm corrections, introduced to avoid the violation of the constraints on the depletion of the hole states in the standard perturbative 2p2h approach, leads in nuclear matter to a dependence of the momentum distribution with the total nucleon number. This unphysical behavior, which in turn makes the depletion to be nonextensive, arises from contributions of disconnected diagrams contained in the norm. It is found that the extensivity is again recovered when the 4p4h excitations in the ground state are included, and a reasonable value for the total number of nucleons promoted above the Fermi level is obtained. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevc.53.1664

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It is shown that the norm corrections, introduced to avoid the violation of the constraints on the depletion of the hole states in the standard perturbative 2p2h approach, leads in nuclear matter to a dependence of the momentum distribution with the total nucleon number. This unphysical behavior, which in turn makes the depletion to be nonextensive, arises from contributions of disconnected diagrams contained in the norm. It is found that the extensivity is again recovered when the 4p4h excitations in the ground state are included, and a reasonable value for the total number of nucleons promoted above the Fermi level is obtained. \textcopyright{} 1996 The American Physical Society.
The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an ab initio description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems.
The self-consistent Green’s function method within the ladder approximation provides a microscopic description of correlated nuclear systems which properly treats the nucleon-nucleon correlations induced by the short-range and tensor components present in any realistic interaction. These correlations produce a sizable depletion of low momenta below the Fermi surface as well as the occupation of high momenta in the nuclear ground state. A few representative results for nuclear matter are presented to illustrate the present progress in the application of this method to nuclear systems.
The theory of the thermodynamic properties of nuclear matter at finite temperatures is developed on the basis of thermodynamic Green functions for a system of interacting nucleons. The influence of the surrounding nuclear matter on the two-nucleon system leads to a weakening of the effective nucleon-nucleon interaction and at the Mott density, which depends on the temperature and total momentum of the two-nucleon system, the bound state disappears. The deuteron degree of association and the phase diagram of nuclear matter are discussed.
A representation of nucleon spectral functions in nuclear matter is developed. Various contributions are identified including a quasiparticle term, broad background contributions below and above the Fermi energy, and a high-energy tail which has no significant momentum dependence. A convenient analytical energy dependence supplemented by a numerical dependence on momentum allows computationally tractable studies of the consequences associated with the considerable dressing of the nucleons. Applications are presented for high-momentum components as a function of energy, density of states, dressed particle-hole response, and the dressed particle-particle/hole-hole propagator.
The generalized momentum distribution n(p,Q), related to the half-diagonal two-body density matrix ${\mathrm{\ensuremath{\rho}}}_{2\mathrm{h}}$(r1{\mathbf{r}}_{1}r1​,r2{\mathbf{r}}_{2}r2​,${\mathbf{r}}_{1}^{\ensuremath{'}}$) by Fourier transformation in the variables r1{\mathbf{r}}_{1}r1​-${\mathbf{r}}_{1}^{\ensuremath{'}}$ and r1{\mathbf{r}}_{1}r1​-r2{\mathbf{r}}_{2}r2​, plays a key role in the description of final-state interactions in the nuclear medium and other strongly interacting many-body systems. The function n(p,Q) is explored for two Jastrow-correlated models of infinite nuclear matter within a Fermi hypernetted-chain procedure. Significant departures from ideal Fermi gas behavior in certain kinematic domains provide signatures of the strong short-range correlations contained in these models. However, such deviations are less prominent than in earlier calculations based on low-order cluster truncations; correspondingly, violations of the sequential relation are greatly reduced. Simple prescriptions for improved low-cluster-order approximations to n(p,Q) are suggested by analysis of the results of the Fermi hypernetted-chain evaluation. These results are also used to assess the quality of Silver's approximation n(p,Q)\ensuremath{\approx}n(p)[S(Q)-1] for the generalized momentum distribution in terms of the ordinary momentum distribution n(p) and the static structure function S(Q), with findings that have potential implications for the interpretation of data from inclusive electron scattering by nuclei at high momentum transfers.